Bosonization, Duality, and the $C$-Theorem in the Non-Abelian Thirring Model

Abstract

We revisit the two dimensional non-Abelian Thirring model in order to investigate its fixed point structure and the corresponding renormalization group (RG) flow. For this purpose we discuss the bosonization of the model, and we present different, but of course equivalent, bosonic versions of the theory. The bosonic theories are illuminating in that they exhibit the fixed points in a manifest way, and also possess a remarkable strong/weak duality that sheds light on the fixed point structure of the theory. We study the RG flow through the computation of the Zamolodchikov $C$-function and of the $\beta$-function in the large-level limit. Within this framework, we discuss how close to the infrared fixed point the RG flow can reach, since this point is strictly unachievable due to an emergent gauge invariance.